Josh has $500 in his savings account. he deposits $25 into his savings account each month. he purchased home theater equipment for $1,600. the store he bought the equipment from offered him a $1,600 interest-free loan for 24 months. he pays off $80 of the loan every month from his checking account (not his savings account). how many months will it take for josh to have enough money in his savings account to pay off the entire outstanding amount for his purchase? round your answer to the nearest whole number. a. 8 months b. 10 months c. 20 months d. 24 months

  B. 10 months

Step-by-step explanation:

The balance on the loan will be ...

  b = 1600 - 80t . . . . . . where t is the number of months of payments

The balance in the savings account will be ...

  s = 500 + 25t

The savings account balance will be at least as much as the loan balance when ...

  s ≥ b

  500 +25t ≥ 1600 -80t . . . substitute the account balance expressions

  105t ≥ 1100 . . . . . . . . . . . . add 80t -500

  t ≥ 1100/105 ≈ 10.48 ≈ 10

It will take Josh 10 months to have enough savings to pay the loan in full.

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Comment on rounding

IMO, it makes no sense to round down, as Josh will NOT have enough in 10 months. He will have enough after he makes one more payment of $80. At 10 months, the loan balance is $50 more than the savings balance. It will be 11 months before there is enough savings to pay off the loan.

↓↓↓↓↓↓↓↓↓

step-by-step explanation:

this is a parabola.

ending amount = beginning amount / (2^n)

where "n" = number of half-lives (or elapsed time / half-life)

ending amount = 50 mg / (2 ^10 / 5.3)

ending amount = 50 mg / (2 ^ 1.8867924528)

ending amount = 50 m / 3.6981210597

ending amount = 13.5203794557 mg

or about 13.5 mg remain

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